<span>Triangle ABC is congruent to triangle DEF
</span>m<A = m<span><D
</span>m<B = m<span><E
</span>m<C = m<span><F
AB = DE
BC = EF
AC = DF
So answer:
</span>m∠C=m∠F
Answer:
The linear speed of the bike is 19.242 miles per hour.
Step-by-step explanation:
If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike (
), measured in inches per second, is:
Where:
- Radius, measured in inches.
- Angular speed, measured in radians per second.
Now, the angular speed must be converted from revolutions per minute into radians per second:
The speed of the bike is: (
and )
Lastly, the outcome is converted into miles per hour:
The linear speed of the bike is 19.242 miles per hour.
ANSWER TO QUESTION 1
.
EXPLANATION
The function given to us is,
According to rational roots theorem,
are possible rational zeros of
.
We find out that,
Also
This implies that
are factors of
and hence 
is also a factor.
We perform the long division as shown in the diagram.
Hence,
.
ANSWER TO QUESTION 2
Sketching the graph
We can see from the factorization that the roots
and 
have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.
Also the root 
has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.
Now we determine the position of the graph on the following intervals,
We can now use these information to sketch the function as shown in diagram
Answer:
Not enough information, need a picture.
Step-by-step explanation:
Let's take a look at the <em>relationship</em> between x and y in this function. When we look at the first non-zero pair, (-1, 1), we can see that, in the transition from x to y, our x value was had to have been multiplied by -1. For now, we could tentatively say that y = -x. Unfortunately, the next pair, (-4, 2), debunks this hypothesis pretty quickly, as 2 ≠ -(-4). We'll need to reexamine the relationship between x and y here.
One patter that we can be fairly confident in is that multiplication by -1; the sign is flipped from negative to positive when we go from x to y in each case, so we can hold onto that component of the function. Something else is happening before that sign flip, though, and we'll need to look into that by seeing how else the numbers are connected.
Ignoring the negative signs for a moment, let's take a look at the pairs (1,1) and (4, 2). We can transform 1 to 1 pretty easily; we simply multiply or divide it by 1. From 4 to 2, we can either divide it by 2 or multiply it by 1/2. Let's thing in terms of division for now. We know that
1/1 = 1 (obviously)
4/2 = 2
We might have something here! It looks like the number we divide by and the number we obtain are the same, so let's explore this further. Multiplying both sides by those denominators, we find:
1 = 1²
4 = 2²
Almost there! To finally find the relationship, we just square root both sides to get:
√1 = 1
√4 = 2
So that was the function we'd been looking for - a square root! Putting that together with what we said about changing the sign at the beginning, we have:
y =√(-x)
To verify this, we just need to plug in a few pairs, and we find that indeed:
1 = √-(-1) = √1 = 1
2 = √-(-4) = √4 = 2
